For $x \in \mathbb{R}$ with $|x| \lt 1$, the value of $\sum_{n=0}^{\infty}(1+n) x^n$ is

• A

  $\frac{x^2+x+1}{(1-x)^2}$.
• B

  $\frac{1}{1-x}$.
• C

  $\frac{x^2-x+1}{(1-x)^2}$.
• Correct answer
  D

  $\frac{1}{(1-x)^2}$.

Hence, the correct answer is option: 'D'.